A Boeing 767-300, Belgium registration OO-CTR, operated by City Bird, experienced cabin decompression, while on a foreign charter flight. Visual meteorological conditions prevailed at the time, and an IFR flight plan was filed. The aircraft sustained substantial damage. The flight had departed Puerto Plata, Dominican Republic, about 1500. According to the captain, while at flight level FL310, a speed of mach .80, he got a warning of cabin altitude, he ran the checklist and performed an emergency descent to FL 100, where fuel was dumped and subsequent landing was performed back at Puerto Plata. No injuries were reported. After landing examination revealed that the left over wing slide compartment door was missing and the slide had disintegrated. Two holes were found in the left aft fuselage skin. In addition, electrical wires were damaged.